Math Forum :: View topic – Ring homomorphisms

Suppose Q = field of rationals, R = ring, f, g: Q -> R are ring homomorphism that maps 1 to the unity (multiplicative identity) of R. Prove f = g. Comment: It is easy to show that if n is an integer, f(n) = g(n). The trickest part is to show f(x) = g(x) in general.

Notice: R may not be a division ring/integral domain.